Relative Speed — Approach & Chase

🎯 Learning Objective

Add speeds for opposite motion, subtract for same direction, and solve meeting and catching problems.

💡 Concept

• Opposite directions → relative speed = SUM (the gap closes fast)
• Same direction → relative speed = DIFFERENCE (a slow chase)
• Time to meet or catch = initial gap ÷ relative speed
• After the meeting point, each side is a fresh D = S × T problem

🧮 Key Formulas

Opposite: v₁ + v₂

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Same: v₁ − v₂

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Time to meet = Gap ÷ Relative speed

✏️ Easy Example

Q. Two cars 200 km apart drive towards each other at 60 km/h and 40 km/h. After how long do they meet?

1. Relative speed = 60 + 40 = 100 km/h
2. Time = 200 ÷ 100

Answer: 2 hours

🇮🇳 Real-Life Example

On the highway, a truck you overtake drifts back slowly while oncoming traffic flashes past in a blink — subtract when parallel, add when head-on. Same physics, felt daily.

📝 Exam-Level Example

Q. A thief runs at 8 km/h. A policeman 100 m behind chases him at 10 km/h. In how much time is the thief caught?

1. Relative speed = 10 − 8 = 2 km/h
2. Gap = 0.1 km
3. Time = 0.1 ÷ 2 = 0.05 h = 3 min

Answer: 3 minutes

📝 Exam-Level Example

Q. Two buses start from towns 300 km apart towards each other at 70 km/h and 50 km/h. How far from the first town do they meet?

1. Meet after 300/(70 + 50) = 2.5 h
2. First bus covers 70 × 2.5

Answer: 175 km

🪄 Memory Trick

Convert the gap and the relative speed into the same units FIRST — then every story collapses to Gap ÷ Relative speed.

⚠️ Common Mistakes

• ❌ Adding speeds in a chase (same direction needs subtraction)
• ❌ Leaving the gap in metres while the speed is in km/h

🏆 Exam Tips

• ✅ Distance covered by each traveller = own speed × meeting time
• ✅ In catch-up problems relative speed automatically accounts for the runner's escape

📌 Summary

• Opposite → add speeds
• Same direction → subtract
• Meet/catch time = gap ÷ relative speed
• Then back to plain D = S × T